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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4, Problem 9RE
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Evaluate the limit.

lim x → 0 e 2 x − e − 2 x ln ( x + 1 )

To determine

To evaluate: The value of limx→0e2x−e−2xln(x+1) .

Explanation

Obtain the value of the function as x approaches 0.

As x approaches 0 the numerator is,

e2x−e−2x=e2(0)−e−2(0)=e0−e0=1−1=0

As x approaches 0 the denominator is,

ln(x+1)=ln(0+1)=ln(1)=0

Thus, limx→0e2x−e−2xln(x+1)=00 is in an indeterminate form.

Therefore, apply L’Hospital’s Rule and obtain the limit as shown below

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Statistics for The Behavioral Sciences (MindTap Course List)

Statistical Literacy (a) What measures of variation indicate spread about the mean? (b) Which graphic display s...

Understanding Basic Statistics

Sketch the graph of the function. 50. g(x) = ||x| 1|

Single Variable Calculus

In problems 29-32, express each inequality or graph using interval notation and name the type of interval. 32. ...

Mathematical Applications for the Management, Life, and Social Sciences

For Problems 1-14, state the property that justifies each of the statements. For example, 3+(4)=(4)+3 because o...

Intermediate Algebra

Sketch the graphs of the equations in Exercises 512. xy=x2+1

Finite Mathematics

Use inductive reasoning to predict the next letter in the following list. O, T, T, F, F, S, S, E, ,,, Hint: Loo...

Mathematical Excursions (MindTap Course List)

a. Draw a line graph of the pmf of X in Exercise 35. Then determine the pmf of X and draw its line graph. From ...

Probability and Statistics for Engineering and the Sciences

Given a demand function p(x), explain what is meant by the consumer surplus when the amount of a commodity curr...

Single Variable Calculus: Early Transcendentals

Use Exhibit 20-5, Corporate Bond Quotation Table, on page 687 to fill in the blanks for Exercises 1-10. EXHIBI...

Contemporary Mathematics for Business & Consumers

Find the area of an equilateral triangle with a sides of length 2.5 m each. b apothem of length 3 in.

Elementary Geometry For College Students, 7e

3. Consider the additive groups of real numbers and complex numbers and define by . Prove that is a homomorph...

Elements Of Modern Algebra

Write each number in engineering notation: 4500

Elementary Technical Mathematics

Graph one complete cycle of each of the following. In each case, label the axes accurately and identify the hor...

Trigonometry (MindTap Course List)

Completing the Square In Exercises 33-36, find the Indefinite integral xx2+6x+12dx

Calculus: Early Transcendental Functions (MindTap Course List)

Sketching Lines In Exercises 13 and 14, sketch the lines through the point with the indicated slopes. Make the ...

Calculus of a Single Variable

In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 8, YX = 10 and WX = 20. Find height h the length of ZD o...

Elementary Geometry for College Students

Find the amount of an ordinary annuity of $120/month for 5 years at 638%/year compounded monthly.

Finite Mathematics for the Managerial, Life, and Social Sciences

Work In Exercises 37-42, find the work done by the force field F on a particle moving along the given path. F(x...

Calculus (MindTap Course List)

log27 9 =

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding an Equation of a PlaneIn Exercises 4556, find an equation of the plane with the given characteristics. ...

Multivariable Calculus

By the method of variation of parameters, a particular solution to, where , and:

Study Guide for Stewart's Multivariable Calculus, 8th

Converting to Polar Coordinates: In Exercises 1726, evaluate the iterated integral by converting to polar coord...

Calculus

Find the area of each of the segments ACE for Exercises 41 through 45.

Mathematics For Machine Technology

The following table shows Googles annual revenue for 2009 to 2014 (The Wall Street Journal, August 2014). Year ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Graph each function using a combination of transformations applied to the graph of a basic function. fx=2x+3 x0

College Algebra (MindTap Course List)

Define a main effect for one factor and an interaction between factors, and be able to identify main effects an...

Research Methods for the Behavioral Sciences (MindTap Course List)

In Exercises , do the following. a. Solve the system of equation. b. Check your solution by substituting it bac...

Mathematics: A Practical Odyssey

Draw a graph for the standard normal distribution. Label the horizontal axis at values of3, 2, 1, 0, 1, 2, and ...

Statistics for Business & Economics, Revised (MindTap Course List)

Identify the circumstances in which it is useful to write a research proposal before conducting the actual rese...

Research Methods for the Behavioral Sciences (MindTap Course List)

Much concern has been expressed regarding the practice of using nitrates as meat preservatives. In one study in...

Introduction To Statistics And Data Analysis

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